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Second-order variational analysis in second-order cone programming. (English) Zbl 1440.90079
Summary: The paper conducts a second-order variational analysis for an important class of nonpolyhedral conic programs generated by the so-called second-order/Lorentz/ice-cream cone $${\mathcal{Q}}$$. From one hand, we prove that the indicator function of $${\mathcal{Q}}$$ is always twice epi-differentiable and apply this result to characterizing the uniqueness of Lagrange multipliers together with an error bound estimate in the general second-order cone programming setting involving twice differentiable data. On the other hand, we precisely calculate the graphical derivative of the normal cone mapping to $${\mathcal{Q}}$$ under the metric subregularity constraint qualification and then give an application of the latter result to a complete characterization of isolated calmness for perturbed variational systems associated with second-order cone programs. The obtained results seem to be the first in the literature in these directions for nonpolyhedral problems without imposing any nondegeneracy assumptions.

##### MSC:
 90C31 Sensitivity, stability, parametric optimization 49J52 Nonsmooth analysis 49J53 Set-valued and variational analysis
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